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The one-dimensional three-state cyclic cellular automaton is a simple spatialmodel with three states in a cyclic "rock-paper-scissors" prey-predatorrelationship. Starting from a random configuration, similar states gather inincreasingly large clusters; asymptotically, any finite region is filled with auniform state that is, after some time, driven out by its predator, each statetaking its turn in dominating the region (heteroclinic cycles).  We consider the situation where each site in the initial configuration ischosen independently at random with a different probability for each state. Weprove that the asymptotic probability that a state dominates a finite regioncorresponds to the initial probability of its prey. The proof methods are basedon discrete probability tools, mainly particle systems and random walks.

Asymptotic behaviour of the one-dimensional "rock-paper-scissors" cyclic cellular automaton